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Stock-Based Compensation (Tables)
 12 Months Ended
Oct. 31, 2024
Share-Based Payment Arrangement [Abstract]  
Summarized Activity Related to Stock Options
The following table summarizes activity related to stock options during 2024:
Number of
Options		Weighted˗Average
Exercise Price
Per Share		Aggregate
Intrinsic
Value		Weighted˗Average
Remaining
Term
Outstanding at October 31, 20231,062 $152.41 
Granted61 $238.35 
Exercised(261)$121.80 
Forfeited or expired(7)$229.54 
Outstanding at October 31, 2024855 $167.26 $70,409 4.7 years
Expected to vest164 $239.44 $2,110 7.8 years
Exercisable at October 31, 2024690 $149.97 $68,283 4.0 years
Summarized Information on Currently Outstanding Options
Summarized information on currently outstanding options follows:
Range of Exercise Price
$67 - $125
$126 - $190
$191 - $268
Number outstanding261 314 280 
Weighted-average remaining contractual life, in years3.04.57.4
Weighted-average exercise price$110.17 $154.44 $235.04 
Number exercisable261 313 116 
Weighted-average exercise price$110.15 $154.36 $227.51 
Fair Value Assumptions of Stock Options
The fair value of each option grant was estimated at the date of the grant using the Black-Scholes option-pricing model with the following assumptions:
202420232022
Expected volatility
30.3%-31.7%
30.4%-31.8%
30.6%-30.8%
Expected dividend yield
1.15%-1.20%
1.12%-1.27%
0.76%-0.89%
Risk-free interest rate
4.22%-4.52%
3.79%-4.21%
1.36%-2.65%
Expected life of the option (in years)
5.0-6.2
5.0-6.2
5.3-6.2
Summarized Activity Related to Restricted Stock Units
The following table summarizes activity related to restricted share units in 2024:
Number of
Units		Weighted˗Average Grant Date Fair
Value
Restricted share units at October 31, 202369 $236.28 
Granted41 $235.53 
Forfeited(6)$241.89 
Vested(37)$229.72 
Restricted share units at October 31, 202467 $238.83 
Summarized Activity Related to Director Deferred Compensation Shares
The following table summarizes activity related to director deferred compensation share equivalent units during 2024:
Number of
Shares		Weighted˗Average
Grant Date Fair
Value Per Share
Outstanding at October 31, 202378 $93.11 
Restricted stock units vested5 $215.81 
Dividend equivalents1 $249.07 
Distributions(19)$54.54 
Outstanding at October 31, 202465 $115.66